On the first 5 quizzes of his physics class, Daniel got an average score of 85. What does he need on the next quiz to have an overall average of 87?
Let his score on the next quiz be $x$ The sum of all of his scores is then $5 \cdot 85 + x$ The same sum must also be equal to $6 \cdot 87$ Solve: $x = 6 \cdot 87 - 5 \cdot 85 = 97$.